📘 Logistic language (Carnap)

=== a constructional system language used to give clear and exact definition of the constructional system==

Symbols

• Constants:
  • classes: lower case, initial letter
  • relations: capital, initial letter
• Variables:
  • classes: a,b
  • relations: P, Q, R
  • general: x, y, z
• Statements:
  • ~: negation
  • ⊃: implication
  • one or several dots: conjunction
  • =: identity
• propositional functions:
  • e.g. $fx$ → ”$fx$ holds for every x”
• Classes
  • ∩: intersection
  • ∪: union
  • ⊂: subsumption
  • -: remainder
  • $\alpha Ex\beta$: “no element in common”
  • $\exists !a$: “a is not empty”
  • $[x]$: the class with only the element x
• Relations
  • ∩: intersection
  • ∪: union
  • ⊂: subsumption
  • $\overrightarrow{R^{\prime }}x$: referents of $x$ in R
    • R: 📕 Relation extension
• 🐶 Quasi Analysis
  • $Sim{l}^{\prime }R$: class of similarity circles based on R
  • $Abst{r}^{\prime }R$: class of abstraction classes based on R
  • Topology: $Dnp(n,a,x,U)$: “a has, in element x, the dimension number n relative to a neighborhood relation U” (Ger: $Dzp(n,a,x,U)$)
  • $Vici{n}^{\prime }Q$: the neighborhood relation, which is determined by the proximity relation Q (Ger: $Umg{r}^{\prime }Q$)
  • $n$ $Dnhomvic$ $Q$; the field of W has the homofenous dimension number n relative to $Vici{n}^{\prime }Q$ (Ger: $n$ $Dzhomum$ $Q$)